Be aware that you can have problems with both systems. The "it just works" is just marketing. It's easy enough to see that a mac computer can have it's own fair share of problems if either you don't know what you're doing or there is a defective piece of hardware in there.
That being said, the mac mini does come with a remote. You will have to purchase a monitor keyboard and mouse with it. I'm not sure the range on the remote, but I don't know if you'd be able to switch tracks from another room. Almost any computer can hookup to your Sony TV if you have the right cables or video card. I wouldn't suggest using a TV as a computer screen as the resolution on a TV is no where near the resolution on a computer monitor and will often leave the image fuzzy and "ugly" looking since the screen size is too large for such a small resolution.
What kind of audio setup do you have?
edit: I sincerely hope that this isn't considered bashing, but Apple does not manufacture all the hardware in their machines. I was putting XP on my MBP last night so I could play a few games when I got bored and when the mac drivers were being installed, you could see pretty much all the hardware. I remember off the top of my head that it had a sigamatel audio device (the same company that makes them for dell's laptops), a matashi (sp?) DVD drive, intel chip of course, and a bunch of other things. Apple just control what goes into their machines and therefore while developing the OS, can write their own drives since there's a very limited selection of hardware to write for in comparison to all the "pc" devices and hardware that can run windows. That's why it's so easy for you to run windows on a mac. OS X has all the drivers included with it, so it's not like when installing windows where you some times have to hunt for drivers for different devices when installing the os.